As mentioned in the introduction, our Theorem REF , together with results from [1]}, [2]}, and [3]}, respectively, implies that \(\mathfrak {a}_{\mathrm {vec},F}\) , \(\mathfrak {a}_e\) , \(\mathfrak {a}_g\) , and \(\mathfrak {a}_p\)  are all equal to \(\mathrm {non}(\mathcal {M})\)  in canonical models, and in particular, to each other. While these cardinals can be separated from \(\mathrm {non}(\mathcal {M})\)  using Shelah's technique [4]} of template iterations, see [5]}, it would be very interesting to find a model in which some of \(\mathfrak {a}_e\) , \(\mathfrak {a}_p\) , \(\mathfrak {a}_g\) , and \(\mathfrak {a}_{\mathrm {vec},F}\)  (for some \(F\) ) are unequal. This question was asked for \(\mathfrak {a}_p\)  and \(\mathfrak {a}_g\)  in [3]}, and we believe that it deserve renewed attention.
